Here we discuss the extremal cases \(s=1\)  and \(s=0\) .
As for \(s=1\) , we are led to consider [1]}, [2]}, [3]} the energy functional
\({\mathcal {F}}^{T}_1(u):=\frac{1}{2T}\int _{0}^T | u^{\prime }(x)|^2 \,\mathrm {d} x .\) 
